All categories

3 years ago

Solve the systems by the addition method x - 2y = - 4 2x + y = 7

Mathematics

1 answer:

vfiekz [6]3 years ago

5 0

To solve this system of equations by addition, our first goal is to cancel

out one of the variables by adding the two equations together.

However, if we add these two equations together right away, nothing

will cancel so we need to set things up so a variable will cancel.

Notice that we have an 2x in our second equation.

If we had a -2x in our first equation, then the x's would cancel out.

In order to create a -2x in the first equation, we simply

multiply both sides of the first equation by -2.

So we have (-2)(x - 2y) = (-4)(-2) which can be rewritten as -2x + 4y = 8.

Now rewrite both equations, as shown below.

Now when we add the equations together, the x terms

will cancel out and we're left with 5y = 15.

Dividing both sides by 5, <em>y = 3</em>.

To solve for x, plug a 3 in for y in either one of our 2 original equations.

So let's go with our second equation.

Plugging a 3 in for y, we get 2x + (3) = 7.

Now subtract 4 from both sides to get 2x = 4.

Dividing both sides by 2, we fid that <em>x = 2</em>.

Since x = 2 and y = 3, our answer is the ordered pair (2, 3).

You might be interested in

2019 Chapter Sprint Round, #20

nadezda [96]

Answer:

$Speed\ of\ car=38\ km/h$

Step-by-step explanation:

Distance Covered by Horse:

$Speed\ of\ horse=50\ km\h=50\times \frac{1000}{60}\ meter/ minute\\\\Speed\ of\ horse=\frac{2500}{3}\ meter/minute\\\\Distance\ covered\ in\ 4\ minutes=speed\times time=\frac{2500}{3}\times 4\\\\Distance\ covered\ in\ 4\ minutes=\frac{10000}{3}\ meters\\\\$

Distance covered by Car:

$Let\ speed\ of\ car=x\ meter/minute\\\\time=4\ minutes\\\\Distance\ covered=speed\times time=4\times x=4x$

$Distance\ covered\ by\ horse=Distance\ covered\ by\ car+800\\\\\frac{10000}{3}=4x+800\\\\4x=\frac{10000}{3}-800\\\\4x=\frac{7600}{3}\\\\x=\frac{7600}{3\times 4}\ meter/minute\\\\x=\frac{7600}{3\times 4}\times \frac{60}{1000}\ km/h\\\\x=38\ km/h$

7 0

3 years ago

HELP ME A INNOCENT CHILD PLEASSSSSSSSSSSE

agasfer [191]

1 YEAR = 12 months

divide: 5,031 ÷ 12 = 419.25

419 dollars and 25 cents each month

hope it helps!

4 0

4 years ago

Read 2 more answers

Mark buys 3 2/5 pounds of apples. He uses 2/3 of the apples in a recipe. Which of the following expressions can be used to find

Dahasolnce [82]

Answer:

Step-by-step explanation:

jayfeather friend me

7 0

3 years ago

Part 3: Write the equation of and graph an ellipse.

tensa zangetsu [6.8K]

Answer:

Step-by-step explanation:

The center is halfway between vertices, at (4, -6).

It is also halfway between foci.

:::::

The vertices are vertically aligned, so the parabola is vertical.

General equation for a vertical ellipse:

(y-k)²/a² + (x-h)²/b² = 1

with

center (h,k)

vertices (h,k±a)

co-vertices (h±b,k)

foci (h,k±c), c² = a²-b²

Apply your data and solve for h, k, a, and b.

center (h,k) = (4, -6)

h = 4

k = -6

vertices (4,-6±a) = (4,-6±9)

a = 9

foci (4,-6±c) = (4,-6±5√2)

b² = a² - c² = 9² - (5√2)² = 31

b = √31

The equation becomes

(y+6)²/81 + (x-4)²/31 = 1

:::::

length of major axis = 2a = 18

length of minor axis = 2b = 2√31

8 0

3 years ago

Haroldo, Xerxes, Regina, Shaindel, Murray, Norah, Stav, Zeke, and Georgia are

anastassius [24]

And this problem, we're trying to figure out the probability that Xerxes arrives first and Regina arrives last. Now, the first thing to note is that there are nine people. So if we list off nine different spaces, there's nine spaces and now the order in which they arrive could be any order. So for the first spot there are nine different ways that someone can show up, Anyone can show up first and then once someone has shown up first, the person who arrives second, there are eight different ways to choose that person. Similarly, the person who arrives third, there are seven people remaining, so there's seven ways to choose that and so on. And so there are actually nine factorial ways that the people can arrive to the party. Now if xerxes needs to be in the first spot and Regina needs to be in the last spot than in these remaining seven spaces, we can put any people, so there can be any ordering between xerxes and Regina. So there is seven factorial ways to order the people between xerxes and Regina. So the probability that we end up with is seven factorial divided by nine factorial. So that is seven factorial. And remember that nine factorial can be written as nine times eight times seven factorial. The seven factorial are going to cancel. We get 1/7 times eight which is equal 1/72 which is equal to approximately zero point 014 and that's it

3 0

2 years ago